Question

A and b can fill a cistern in 7.5 minutes and 5 minutes respectively and c can carry off 42 litres per minute. if the cistern is already full and all the three pipes are opened, then it is emptied in 1 hour. how many litres can it hold?

Answer 1

Answer:

Step-by-step explanation:

A and B can fill up the cistern in 7.5 minutes & 5 minutes respectively. C can fill up 14 liters per minute.

The capacity of cistern is denoted as l liters. Water filled in one hour = l/7.5 * 60 + l/5*60 = 20 l.

Water removed in one hour = 14x60. Since, the tank was full initially thus, l + 20l – 14X 20 = 0. L= 40 liters.

Hope it helps u^__^

Answer 2

Q. A and b can fill a cistern in 7.5 minutes and 5 minutes respectively and c can carry off 42 litres per minute. if the cistern is already full and all the three pipes are opened, then it is emptied in 1 hour. how many litres can it hold?

Ans:- 40 litres

Explanation:-

Given :-

Time taken by A to fill the Cistern =

7.5 Min

Time taken by B to fill the cistern = 5 min.

$let \: the \: capacity \: of \: cistern \: b e\:\: = v$

$then \: rate \: at \: which \: a \: can \: fill \: it \: = \frac{v}{ \frac{15}{2} } = \frac{2v}{15}$

$rate \: at \: which \: \: pipe \: b \: can \: fill = \frac{v}{5}$

$rate \: of \: water \: dissipiated \: by \: pipe \: c = 42$

$since \: tank \: get \: empty \: in \: 1 \: hr$

$time \: taken \: by \: pipe \: c \: = 14 \times 60 = 840$

Since,

$volume \: of \: tank \: + volume \: filled \: by \: pipe \: a \: + volume \: filled \: by \: pipe \: b = volume \: drained \: by \: pipe \: c$

$v + 60 \times \frac{2v}{15} + 60 \times \frac{v}{5} = 84 0$

$v + 8v + 12v = 840$

$21v = 840$

$v = 40l$